Details

sample29.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify111.0ms

Counts: 1 → 1

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.4b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z (/ 1692356830115869.0 281474976710656.0)) z)
0.1b	(* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z)
4.0b	(* y (+ (* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z) (/ 5029535718965825.0 18014398509481984.0)))
23.4b	(/ (* y (+ (* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z) (/ 5029535718965825.0 18014398509481984.0))) (+ (* (+ z (/ 1692356830115869.0 281474976710656.0)) z) (/ 7544303578448747.0 2251799813685248.0)))

rewrite343.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
14×	`*-un-lft-identity`
13×	`associate-r/` `associate-l/`
12×	`add-cube-cbrt`
11×	`frac-add`
10×	`pow1` `associate-l`
9×	`associate-r`
8×	`flip3-+` `flip-+`
5×	`associate-/l/`
4×	`prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`times-frac` `pow-prod-down` `associate-/r` `-commutative` `unswap-sqr`
2×	`cbrt-undiv` `div-exp`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 97

Calls

4 calls:

61.0ms	(* (+ z (/ 1692356830115869.0 281474976710656.0)) z)
53.0ms	(* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z)
129.0ms	(* y (+ (* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z) (/ 5029535718965825.0 18014398509481984.0)))
95.0ms	(/ (* y (+ (* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z) (/ 5029535718965825.0 18014398509481984.0))) (+ (* (+ z (/ 1692356830115869.0 281474976710656.0)) z) (/ 7544303578448747.0 2251799813685248.0)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (+ z (/ 1692356830115869.0 281474976710656.0)) z)
98.0ms	(* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z)
58.0ms	(* y (+ (* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z) (/ 5029535718965825.0 18014398509481984.0)))
141.0ms	(/ (* y (+ (* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z) (/ 5029535718965825.0 18014398509481984.0))) (+ (* (+ z (/ 1692356830115869.0 281474976710656.0)) z) (/ 7544303578448747.0 2251799813685248.0)))

simplify73.0ms

Counts: 109 → 109

prune517.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z (/ 1692356830115869.0 281474976710656.0)) z)
0.1b	(* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z)
0.1b	(* y (/ (+ (* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z) (/ 5029535718965825.0 18014398509481984.0)) (+ (* (+ z (/ 1692356830115869.0 281474976710656.0)) z) (/ 7544303578448747.0 2251799813685248.0))))
18.8b	(/ (+ (* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z) (/ 5029535718965825.0 18014398509481984.0)) (+ (* (+ z (/ 1692356830115869.0 281474976710656.0)) z) (/ 7544303578448747.0 2251799813685248.0)))

rewrite427.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt`
23×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
12×	`associate-*l/`
10×	`pow1` `associate-l`
9×	`frac-add`
8×	`flip3-+` `associate-/r/` `flip-+`
5×	`associate-/l/`
4×	`prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`associate-r/` `pow-prod-down` `associate-/r` `-commutative` `associate-/l`
2×	`cbrt-undiv` `div-exp` `div-inv`
1×	`frac-2neg` `clear-num` `distribute-lft-out`

Counts

4 → 114

Calls

4 calls:

62.0ms	(* (+ z (/ 1692356830115869.0 281474976710656.0)) z)
70.0ms	(* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z)
163.0ms	(* y (/ (+ (* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z) (/ 5029535718965825.0 18014398509481984.0)) (+ (* (+ z (/ 1692356830115869.0 281474976710656.0)) z) (/ 7544303578448747.0 2251799813685248.0))))
128.0ms	(/ (+ (* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z) (/ 5029535718965825.0 18014398509481984.0)) (+ (* (+ z (/ 1692356830115869.0 281474976710656.0)) z) (/ 7544303578448747.0 2251799813685248.0)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (+ z (/ 1692356830115869.0 281474976710656.0)) z)
77.0ms	(* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z)
153.0ms	(* y (/ (+ (* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z) (/ 5029535718965825.0 18014398509481984.0)) (+ (* (+ z (/ 1692356830115869.0 281474976710656.0)) z) (/ 7544303578448747.0 2251799813685248.0))))
92.0ms	(/ (+ (* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z) (/ 5029535718965825.0 18014398509481984.0)) (+ (* (+ z (/ 1692356830115869.0 281474976710656.0)) z) (/ 7544303578448747.0 2251799813685248.0)))

simplify87.0ms

Counts: 126 → 126

prune526.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z (/ 1692356830115869.0 281474976710656.0)) z)
0.1b	(* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z)
0.3b	(/ y (/ (+ (* (+ z (/ 1692356830115869.0 281474976710656.0)) z) (/ 7544303578448747.0 2251799813685248.0)) (+ (* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z) (/ 5029535718965825.0 18014398509481984.0))))
18.8b	(/ (+ (* (+ z (/ 1692356830115869.0 281474976710656.0)) z) (/ 7544303578448747.0 2251799813685248.0)) (+ (* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z) (/ 5029535718965825.0 18014398509481984.0)))

rewrite427.0ms

Algorithm

rewrite-expression-head

Rules

99×	`times-frac`
67×	`add-sqr-sqrt`
65×	`*-un-lft-identity`
63×	`add-cube-cbrt`
26×	`associate-/r/`
23×	`frac-add`
22×	`associate-*l/`
21×	`associate-/r*`
15×	`add-exp-log` `add-cbrt-cube`
14×	`flip3-+` `flip-+`
8×	`pow1`
7×	`associate-l`
6×	`associate-r/` `associate-r` `div-inv` `associate-/l`
4×	`cbrt-undiv` `div-exp` `associate-/l/` `add-log-exp`
2×	`frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-lft-out`

Counts

4 → 168

Calls

4 calls:

59.0ms	(* (+ z (/ 1692356830115869.0 281474976710656.0)) z)
56.0ms	(* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z)
120.0ms	(/ y (/ (+ (* (+ z (/ 1692356830115869.0 281474976710656.0)) z) (/ 7544303578448747.0 2251799813685248.0)) (+ (* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z) (/ 5029535718965825.0 18014398509481984.0))))
177.0ms	(/ (+ (* (+ z (/ 1692356830115869.0 281474976710656.0)) z) (/ 7544303578448747.0 2251799813685248.0)) (+ (* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z) (/ 5029535718965825.0 18014398509481984.0)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (+ z (/ 1692356830115869.0 281474976710656.0)) z)
76.0ms	(* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z)
157.0ms	(/ y (/ (+ (* (+ z (/ 1692356830115869.0 281474976710656.0)) z) (/ 7544303578448747.0 2251799813685248.0)) (+ (* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z) (/ 5029535718965825.0 18014398509481984.0))))
113.0ms	(/ (+ (* (+ z (/ 1692356830115869.0 281474976710656.0)) z) (/ 7544303578448747.0 2251799813685248.0)) (+ (* (+ (* z (/ 4992947066835229.0 7.205759403792794e+16)) (/ 4429125951667411.0 9007199254740992.0)) z) (/ 5029535718965825.0 18014398509481984.0)))

simplify161.0ms

Counts: 180 → 180

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 7289022650859423.0 18014398509481984.0) (/ y (pow z 2)))
0.2b	(* (/ 1353279196958449.0 18014398509481984.0) (/ y z))
2.5b	(- (+ (* (/ 1353279196958449.0 18014398509481984.0) (/ y z)) (* (/ 4992947066835229.0 7.205759403792794e+16) y)) (* (/ 7289022650859423.0 18014398509481984.0) (/ y (pow z 2))))
8.3b	(/ y (pow z 2))

rewrite252.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt`
92×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
45×	`add-exp-log`
41×	`associate-r`
30×	`add-cbrt-cube`
26×	`associate-l`
23×	`unpow-prod-down`
19×	`associate-*l/`
17×	`div-exp`
15×	`frac-sub`
14×	`unswap-sqr`
12×	`prod-exp`
10×	`frac-times` `associate-*r/`
9×	`cbrt-undiv` `frac-add` `unpow2` `add-log-exp` `sqr-pow`
8×	`pow1` `associate-/r*` `cbrt-unprod`
5×	`div-inv`
3×	`pow-to-exp` `flip3-+` `pow-exp` `flip-+` `associate-/l*`
2×	`diff-log` `pow-prod-down` `*-commutative`
1×	`sub-neg` `flip3--` `frac-2neg` `associate--l+` `clear-num` `sum-log` `flip--`

Counts

4 → 203

Calls

4 calls:

66.0ms	(* (/ 7289022650859423.0 18014398509481984.0) (/ y (pow z 2)))
27.0ms	(* (/ 1353279196958449.0 18014398509481984.0) (/ y z))
131.0ms	(- (+ (* (/ 1353279196958449.0 18014398509481984.0) (/ y z)) (* (/ 4992947066835229.0 7.205759403792794e+16) y)) (* (/ 7289022650859423.0 18014398509481984.0) (/ y (pow z 2))))
10.0ms	(/ y (pow z 2))

series172.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (/ 7289022650859423.0 18014398509481984.0) (/ y (pow z 2)))
21.0ms	(* (/ 1353279196958449.0 18014398509481984.0) (/ y z))
79.0ms	(- (+ (* (/ 1353279196958449.0 18014398509481984.0) (/ y z)) (* (/ 4992947066835229.0 7.205759403792794e+16) y)) (* (/ 7289022650859423.0 18014398509481984.0) (/ y (pow z 2))))
41.0ms	(/ y (pow z 2))

simplify56.0ms

Counts: 215 → 215

prune891.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes357.0ms

Accuracy

98.3% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 16.4b

bsearch298.0ms

Steps

Iters	Range		Point
8	2.1093622585650095e-09	1.6295748548243586e-06	1.611737647351516e-06
8	-1.4853052640572707e+23	-2.4955120319962723e+20	-2.5222447088418515e+20

simplify167.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.2s

8000×

body

valid