Details

analyze507.0ms

Algorithm: search

sample22.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify58.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	10
1	64	10
2	143	10
3	288	10
4	443	10
5	563	10
6	648	10
7	817	10
8	1060	10
9	1066	10
10	1066	10

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 19.9b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
2.7b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
19.2b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

6.0ms	(* (+ z 6.012459259764103) z)
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
9.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
17.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series46.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (+ z 6.012459259764103) z)
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
11.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
24.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify68.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	525	728
1	2508	623
2	5001	623

prune143.0ms

Filtered

68 candidates to 100 candidates (-47.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	4	101

Merged error: 0b

Counts

101 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.1b	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
15.8b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

6.0ms	(* (+ z 6.012459259764103) z)
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
15.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
14.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series41.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* (+ z 6.012459259764103) z)
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
24.0ms	(* y (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))
6.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify73.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	545	1085
1	2456	970
2	5002	970

prune172.0ms

Filtered

84 candidates to 118 candidates (-40.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	118	4	122

Merged error: 0b

Counts

122 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
0.3b	(/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))
15.9b	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
64×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
60×	`add-cube-cbrt`
18×	`associate-/r*`
15×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r/`
8×	`pow1` `flip3-+` `flip-+`
7×	`associate-l`
6×	`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` `associate-/l/` `unswap-sqr`
1×	`distribute-lft-out`

Counts

4 → 150

Calls

4 calls:

6.0ms	(* (+ z 6.012459259764103) z)
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
17.0ms	(/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))
13.0ms	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

series41.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (+ z 6.012459259764103) z)
6.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
25.0ms	(/ y (/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)))
6.0ms	(/ (+ (* (+ z 6.012459259764103) z) 3.350343815022304) (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))

simplify95.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	733	2059
1	3325	1939
2	5002	1937

prune297.0ms

Filtered

126 candidates to 162 candidates (-28.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	162	4	166

Merged error: 0b

Counts

166 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- 14.431876219268938 (* 15.646356830292035 (/ 1 z))) (/ (/ 101.23733352003816 z) z))
0.1b	(/ (/ 101.23733352003816 z) z)
0.3b	(* 15.646356830292035 (/ 1 z))
4.6b	(/ y (+ (- 14.431876219268938 (* 15.646356830292035 (/ 1 z))) (/ (/ 101.23733352003816 z) z)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

98×	`times-frac`
74×	`*-un-lft-identity`
70×	`add-sqr-sqrt`
63×	`add-cube-cbrt`
20×	`add-exp-log`
16×	`add-cbrt-cube` `associate-/l*`
13×	`associate-r`
9×	`add-log-exp`
7×	`associate-/r*` `div-inv`
6×	`pow1` `div-exp`
5×	`cbrt-undiv` `distribute-lft-out`
4×	`frac-add` `prod-exp` `associate-/r/`
3×	`associate-l` `unswap-sqr`
2×	`associate-+l+` `flip3--` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip--` `cbrt-unprod` `flip-+`
1×	`+-commutative` `associate-+l-` `sub-neg` `rec-exp` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `associate-/l/`

Counts

4 → 159

Calls

4 calls:

16.0ms	(+ (- 14.431876219268938 (* 15.646356830292035 (/ 1 z))) (/ (/ 101.23733352003816 z) z))
6.0ms	(/ (/ 101.23733352003816 z) z)
7.0ms	(* 15.646356830292035 (/ 1 z))
15.0ms	(/ y (+ (- 14.431876219268938 (* 15.646356830292035 (/ 1 z))) (/ (/ 101.23733352003816 z) z)))

series23.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (- 14.431876219268938 (* 15.646356830292035 (/ 1 z))) (/ (/ 101.23733352003816 z) z))
3.0ms	(/ (/ 101.23733352003816 z) z)
2.0ms	(* 15.646356830292035 (/ 1 z))
15.0ms	(/ y (+ (- 14.431876219268938 (* 15.646356830292035 (/ 1 z))) (/ (/ 101.23733352003816 z) z)))

simplify77.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	739	1244
1	2984	1135
2	5002	1114

prune207.0ms

Filtered

119 candidates to 171 candidates (-43.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	171	4	175

Merged error: 0b

Counts

175 → 4

regimes197.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.1b

bsearch231.0ms

Steps

Iters	Range		Point
7	42539.73819806787	7010805.270935861	652253.8351324133
9	-3.9900860466595837e+90	-9.988640783056486e+84	-3.952939297273601e+90

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	19
1	53	19

end0.0ms

analyze507.0ms

Algorithm: search

sample593.0ms

Algorithm

intervals

Results

425.0ms

8000×

body

valid

Details

analyze507.0ms

sample22.0ms

simplify58.0ms

prune3.0ms

localize13.0ms

rewrite41.0ms

series46.0ms

simplify68.0ms

prune143.0ms

localize17.0ms

rewrite45.0ms

series41.0ms

simplify73.0ms

prune172.0ms

localize13.0ms

rewrite48.0ms

series41.0ms

simplify95.0ms

prune297.0ms

localize11.0ms

rewrite50.0ms

series23.0ms

simplify77.0ms

prune207.0ms

regimes197.0ms

bsearch231.0ms

simplify2.0ms

end0.0ms

analyze507.0ms

sample593.0ms

Profiling