Details

sample195.0ms

Algorithm

intervals

Results

94.0ms	90×	body	2560	valid
55.0ms	100×	body	1280	valid
12.0ms	39×	body	640	valid
7.0ms	132×	body	80	overflowed
7.0ms	388×	pre	80	true
1.0ms	6×	body	320	valid
1.0ms	20×	body	80	valid
0.0ms	1×	body	160	valid

simplify107.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	40	13
1	101	13
2	258	13
3	766	13
4	3895	13
5	5001	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.7b	(- (exp (* a eps)) 1.0)
3.3b	(- (exp (* b eps)) 1.0)
5.5b	(- (exp (* (+ a b) eps)) 1.0)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
45×	`prod-diff`
39×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-log-exp`
9×	`flip3--` `fma-neg` `flip--`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`sub-neg` `associate-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`diff-log`
2×	`associate-r/` `associate-l/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

27.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
5.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series171.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
34.0ms	(- (exp (* a eps)) 1.0)
31.0ms	(- (exp (* b eps)) 1.0)
52.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify69.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	488	1660
1	2051	1241
2	5003	1216

prune500.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 56.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (fma (sqrt (exp (* a eps))) (sqrt (exp (* a eps))) (- 1.0)) (- (exp (* b eps)) 1.0))
2.7b	(fma (sqrt (exp (* a eps))) (sqrt (exp (* a eps))) (- 1.0))
3.3b	(- (exp (* b eps)) 1.0)
5.5b	(- (exp (* (+ a b) eps)) 1.0)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`associate-r`
4×	`expm1-log1p-u` `sub-neg` `log1p-expm1-u`
3×	`flip3--` `associate-l` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`diff-log` `associate-*r/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 112

Calls

4 calls:

15.0ms	(* (fma (sqrt (exp (* a eps))) (sqrt (exp (* a eps))) (- 1.0)) (- (exp (* b eps)) 1.0))
0.0ms	(fma (sqrt (exp (* a eps))) (sqrt (exp (* a eps))) (- 1.0))
5.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series242.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (fma (sqrt (exp (* a eps))) (sqrt (exp (* a eps))) (- 1.0)) (- (exp (* b eps)) 1.0))
82.0ms	(fma (sqrt (exp (* a eps))) (sqrt (exp (* a eps))) (- 1.0))
32.0ms	(- (exp (* b eps)) 1.0)
50.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	389	1737
1	1506	1122
2	5001	1089

prune451.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 56.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (fma (sqrt (exp (* a eps))) (sqrt (exp (* a eps))) (- 1.0)) (* (+ (sqrt (exp (* b eps))) (sqrt 1.0)) (- (sqrt (exp (* b eps))) (sqrt 1.0))))
2.7b	(fma (sqrt (exp (* a eps))) (sqrt (exp (* a eps))) (- 1.0))
3.4b	(- (sqrt (exp (* b eps))) (sqrt 1.0))
5.5b	(- (exp (* (+ a b) eps)) 1.0)

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

189×	`prod-diff` `sqrt-prod`
152×	`distribute-rgt-in` `distribute-lft-in`
144×	`add-sqr-sqrt`
140×	`*-un-lft-identity`
134×	`add-cube-cbrt`
10×	`associate-*r/`
9×	`pow1` `add-exp-log` `fma-neg` `add-cbrt-cube`
8×	`add-log-exp`
6×	`sub-neg`
5×	`flip3--` `flip--` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`flip3-+` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+` `distribute-lft-out--`
2×	`diff-log` `associate-*l/`
1×	`associate-r` `*-commutative` `fma-udef`

Counts

4 → 280

Calls

4 calls:

66.0ms	(* (fma (sqrt (exp (* a eps))) (sqrt (exp (* a eps))) (- 1.0)) (* (+ (sqrt (exp (* b eps))) (sqrt 1.0)) (- (sqrt (exp (* b eps))) (sqrt 1.0))))
0.0ms	(fma (sqrt (exp (* a eps))) (sqrt (exp (* a eps))) (- 1.0))
9.0ms	(- (sqrt (exp (* b eps))) (sqrt 1.0))
6.0ms	(- (exp (* (+ a b) eps)) 1.0)

series390.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(* (fma (sqrt (exp (* a eps))) (sqrt (exp (* a eps))) (- 1.0)) (* (+ (sqrt (exp (* b eps))) (sqrt 1.0)) (- (sqrt (exp (* b eps))) (sqrt 1.0))))
82.0ms	(fma (sqrt (exp (* a eps))) (sqrt (exp (* a eps))) (- 1.0))
59.0ms	(- (sqrt (exp (* b eps))) (sqrt 1.0))
46.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify89.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1115	10097
1	5002	6662

prune762.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 55.5b

localize34.0ms

Local error

Found 4 expressions with local error:

2.7b	(fma (sqrt (exp (* a eps))) (sqrt (exp (* a eps))) (- 1.0))
3.4b	(- (sqrt (exp (* b eps))) (sqrt 1.0))
5.5b	(- (exp (* (+ a b) eps)) 1.0)
5.5b	(log (exp (- (exp (* (+ a b) eps)) 1.0)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
54×	`prod-diff`
53×	`*-un-lft-identity`
45×	`add-cube-cbrt` `sqrt-prod`
14×	`log-prod`
11×	`exp-sum`
9×	`fma-neg`
8×	`add-log-exp`
6×	`log-pow` `difference-of-squares`
5×	`pow1` `exp-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
3×	`sub-neg`
2×	`flip3--` `diff-log` `flip--`
1×	`log-div` `exp-diff` `rem-log-exp` `fma-udef`

Counts

4 → 131

Calls

4 calls:

0.0ms	(fma (sqrt (exp (* a eps))) (sqrt (exp (* a eps))) (- 1.0))
9.0ms	(- (sqrt (exp (* b eps))) (sqrt 1.0))
5.0ms	(- (exp (* (+ a b) eps)) 1.0)
12.0ms	(log (exp (- (exp (* (+ a b) eps)) 1.0)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(fma (sqrt (exp (* a eps))) (sqrt (exp (* a eps))) (- 1.0))
58.0ms	(- (sqrt (exp (* b eps))) (sqrt 1.0))
44.0ms	(- (exp (* (+ a b) eps)) 1.0)
52.0ms	(log (exp (- (exp (* (+ a b) eps)) 1.0)))

simplify52.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	455	1766
1	1339	1257
2	5002	1109

prune555.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 55.5b

regimes233.0ms

Accuracy

29.6% (1.9b remaining)

Error of 58.7b against oracle of 56.8b and baseline of 59.5b

bsearch277.0ms

Steps

Iters	Range		Point
8	2.5395121883065248e-24	5.7880101574957725e-21	2.5756149971396786e-24
9	-3.125122124602746e+43	-3.596465999237397e+36	-3.6563033602620086e+36

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	42
1	58	42

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.1s	2952×	body	2560	valid
1.8s	3335×	body	1280	valid
273.0ms	882×	body	640	valid
236.0ms	4271×	body	80	overflowed
211.0ms	12272×	pre	80	true
44.0ms	211×	body	320	valid
34.0ms	575×	body	80	valid
6.0ms	46×	body	160	valid