Details

sample30.0ms

Algorithm

intervals

Results

9.0ms	240×	body	80	valid
5.0ms	13×	body	1280	valid
2.0ms	14×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	3×	body	2560	valid
1.0ms	6×	body	160	valid

simplify54.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	23	6
1	46	5
2	128	5
3	362	5
4	1024	5
5	2296	5
6	5001	5

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 15.5b

Counts

2 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
15.6b	(fma (- y z) (/ (- t x) (- a z)) x)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

8.0ms	(/ (- t x) (- a z))
1.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

series145.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/ (- t x) (- a z))
93.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

simplify61.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	268	450
1	733	425
2	2490	423
3	5001	421

prune202.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	55	15	70
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	56	16	72

Merged error: 7.1b

Counts

72 → 16

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.6b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.2b	(* (- y z) (/ (- t x) (- a z)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
74×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
28×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`expm1-log1p-u` `fma-def` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 128

Calls

3 calls:

11.0ms	(/ (- t x) (- a z))
4.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
17.0ms	(* (- y z) (/ (- t x) (- a z)))

series328.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ (- t x) (- a z))
149.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
129.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify64.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	488	901
1	2066	849
2	5001	847

prune305.0ms

Filtered

137 candidates to 95 candidates (69.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	126	11	137
Fresh	10	5	15
Picked	1	0	1
Done	0	0	0
Total	137	16	153

Merged error: 4.1b

Counts

153 → 16

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(* (cbrt (- a z)) (cbrt (- a z)))
0.9b	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
9.0b	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
33×	`cbrt-prod`
26×	`cbrt-div`
24×	`add-exp-log`
21×	`associate-r`
16×	`add-cube-cbrt`
15×	`flip3--` `flip--`
14×	`add-cbrt-cube`
13×	`pow1` `associate-l`
10×	`frac-times` `swap-sqr` `prod-exp` `cbrt-unprod`
8×	`associate-/r/` `distribute-lft-out--`
7×	`pow1/3`
6×	`associate-*l/` `add-log-exp` `difference-of-squares` `unswap-sqr`
5×	`associate-*r/`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-def` `pow-prod-down`
2×	`times-frac` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sum-log` `flip-+` `div-inv`

Counts

4 → 137

Calls

4 calls:

5.0ms	(cbrt (- a z))
10.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
24.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
4.0ms	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series690.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(cbrt (- a z))
125.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
276.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
149.0ms	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify107.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	788	1782
1	3543	1551
2	5001	1434

prune467.0ms

Filtered

149 candidates to 105 candidates (70.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	0	15	15
Picked	1	0	1
Done	0	0	0
Total	148	17	165

Merged error: 4.1b

Counts

165 → 17

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.3b	(* (- t x) (/ 1 (- a z)))
15.4b	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-l` `associate-/r*`
4×	`flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

3 → 105

Calls

3 calls:

5.0ms	(/ 1 (- a z))
13.0ms	(* (- t x) (/ 1 (- a z)))
1.0ms	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

series175.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ 1 (- a z))
52.0ms	(* (- t x) (/ 1 (- a z)))
89.0ms	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

simplify50.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	350	602
1	1497	525
2	5001	481

prune198.0ms

Filtered

114 candidates to 72 candidates (63.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	114	17	131

Merged error: 4.1b

Counts

131 → 17

regimes410.0ms

Accuracy

30.4% (7.9b remaining)

Error of 11.7b against oracle of 3.8b and baseline of 15.1b

bsearch165.0ms

Steps

Iters	Range		Point
6	1.422043756923672e+143	1.1021183756554893e+144	3.6401329854089557e+143
7	-2.5281410119806125e-304	-9.791293333671652e-306	-2.428428164289388e-304
8	-6.082213962958543e-142	-2.3281300819889513e-144	-4.052838434489653e-143
9	-1.307601682434604e+146	-6.54581261410613e+138	-8.790845868670712e+144

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	26
1	39	26

end0.0ms

sample778.0ms

Algorithm

intervals

Results

305.0ms	7758×	body	80	valid
69.0ms	493×	body	640	valid
54.0ms	306×	body	1280	valid
46.0ms	411×	body	320	valid
19.0ms	258×	body	160	valid
5.0ms	21×	body	2560	valid