Details

sample26.0ms

Algorithm

intervals

Results

13.0ms

256×

body

valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	452	21
1	452	21

prune11.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 19.4b

Counts

2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (+ z 6.012459259764103))
0.1b	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
0.1b	(* y (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
18.8b	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

6.0ms	(* z (+ z 6.012459259764103))
6.0ms	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
16.0ms	(* y (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
14.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

series38.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* z (+ z 6.012459259764103))
6.0ms	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
23.0ms	(* y (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))
5.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

simplify74.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4972	1944
1	4972	1944

prune203.0ms

Filtered

89 candidates to 122 candidates (-37.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	117	5	122
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	118	6	124

Merged error: 0b

Counts

124 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

9.7b	(* (/ y (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
17.9b	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
17.9b	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
18.0b	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
66×	`times-frac`
47×	`add-cube-cbrt` `*-un-lft-identity`
42×	`sqrt-prod`
24×	`associate-r` `associate-l`
18×	`add-exp-log` `add-cbrt-cube`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 150

Calls

4 calls:

35.0ms	(* (/ y (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
6.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
6.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
14.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (/ y (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))) (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
3.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
4.0ms	(sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304))
7.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (sqrt (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))

simplify49.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5155	4141

prune361.0ms

Filtered

117 candidates to 162 candidates (-38.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	162	6	168

Merged error: 0b

Counts

168 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
0.1b	(* y (exp (log (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))))
0.5b	(exp (log (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
18.8b	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

rewrite247.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
32×	`log-prod` `exp-sum`
31×	`add-cube-cbrt` `*-un-lft-identity`
28×	`times-frac`
21×	`associate-r`
10×	`add-cbrt-cube`
9×	`pow1` `add-exp-log`
6×	`associate-l` `associate-/r/`
5×	`flip3-+` `flip-+`
4×	`exp-prod` `add-log-exp` `unswap-sqr`
3×	`associate-r/` `associate-/r` `div-inv` `associate-/l*`
2×	`log-div` `exp-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate-/l/`
1×	`cbrt-undiv` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `div-exp` `clear-num` `log-pow` `rem-exp-log`

Counts

4 → 117

Calls

4 calls:

199.0ms	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
18.0ms	(* y (exp (log (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))))
12.0ms	(exp (log (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
13.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

series40.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* z (+ (* z 0.0692910599291889) 0.4917317610505968))
23.0ms	(* y (exp (log (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304)))))
5.0ms	(exp (log (/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))))
6.0ms	(/ (+ (* z (+ (* z 0.0692910599291889) 0.4917317610505968)) 0.279195317918525) (+ (* z (+ z 6.012459259764103)) 3.350343815022304))

simplify39.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5078	2587

prune248.0ms

Filtered

99 candidates to 129 candidates (-30.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	129	6	135

Merged error: 0b

Counts

135 → 6

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 0.07512208616047561 (/ 0.40462203869992125 z))
0.0b	(+ (* 0.0692910599291889 y) (* (/ y z) (- 0.07512208616047561 (/ 0.40462203869992125 z))))
0.2b	(* (/ y z) (- 0.07512208616047561 (/ 0.40462203869992125 z)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`associate-l`
12×	`times-frac`
11×	`add-cube-cbrt`
8×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-r`
5×	`pow1` `sub-neg`
4×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `difference-of-squares`
3×	`flip3--` `flip--`
2×	`frac-times` `associate-*r/` `prod-exp` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `sum-log` `-commutative` `flip-+` `div-inv`

Counts

3 → 73

Calls

3 calls:

6.0ms	(- 0.07512208616047561 (/ 0.40462203869992125 z))
4.0ms	(+ (* 0.0692910599291889 y) (* (/ y z) (- 0.07512208616047561 (/ 0.40462203869992125 z))))
12.0ms	(* (/ y z) (- 0.07512208616047561 (/ 0.40462203869992125 z)))

series20.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(- 0.07512208616047561 (/ 0.40462203869992125 z))
9.0ms	(+ (* 0.0692910599291889 y) (* (/ y z) (- 0.07512208616047561 (/ 0.40462203869992125 z))))
8.0ms	(* (/ y z) (- 0.07512208616047561 (/ 0.40462203869992125 z)))

simplify42.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4996	967
1	4996	967

prune86.0ms

Filtered

57 candidates to 82 candidates (-43.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	82	6	88

Merged error: 0b

Counts

88 → 6

regimes245.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 15.7b

bsearch41.0ms

Steps

Iters	Range		Point
11	436.86900833278656	6.082959852081883e+22	531211.8344037844
7	-667678.649786172	-5486.906575454437	-596675.317596172

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	45
1	49	45

end0.0ms

sample722.0ms

Algorithm

intervals

Results

437.0ms

8000×

body

valid

Details

sample26.0ms

simplify11.0ms

prune11.0ms

localize18.0ms

rewrite45.0ms

series38.0ms

simplify74.0ms

prune203.0ms

localize16.0ms

rewrite67.0ms

series37.0ms

simplify49.0ms

prune361.0ms

localize17.0ms

rewrite247.0ms

series40.0ms

simplify39.0ms

prune248.0ms

localize10.0ms

rewrite25.0ms

series20.0ms

simplify42.0ms

prune86.0ms

regimes245.0ms

bsearch41.0ms

simplify3.0ms

end0.0ms

sample722.0ms

Profiling