Details

sample377.0ms

Algorithm

intervals

Results

190.0ms	85×	body	1280	valid
67.0ms	20×	body	2560	valid
66.0ms	63×	body	640	valid
24.0ms	29×	body	320	valid
10.0ms	46×	body	80	valid
7.0ms	13×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize25.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (tan (+ x eps)) (tan x))
4.3b	(tan (+ x eps))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`tan-quot` `add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `tan-sum` `add-cbrt-cube` `add-exp-log` `frac-sub` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 43

Calls

2 calls:

26.0ms	(- (tan (+ x eps)) (tan x))
10.0ms	(tan (+ x eps))

series189.0ms

Counts

2 → 6

Calls

2 calls:

123.0ms	(- (tan (+ x eps)) (tan x))
66.0ms	(tan (+ x eps))

simplify3.1s

Counts

49 → 49

Iterations

Iter	Nodes
4	3889
3	1289
2	437
1	203
0	96

prune570.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
61×	`times-frac`
54×	`prod-diff`
18×	`fma-neg`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`tan-quot`
8×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1` `flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r` `fma-def` `associate-r` `associate-l*` `associate-/l/`
2×	`flip3-+` `frac-add` `flip-+` `difference-of-squares`
1×	`frac-times` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 173

Calls

4 calls:

28.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
14.0ms	(+ (tan x) (tan eps))
16.0ms	(* (tan x) (tan eps))
103.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.0s

Counts

4 → 12

Calls

4 calls:

306.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
128.0ms	(+ (tan x) (tan eps))
119.0ms	(* (tan x) (tan eps))
458.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.8s

Counts

185 → 185

Iterations

Iter	Nodes
3	5442
2	1570
1	577
0	242

prune2.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.9b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
3.5b	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt`
8×	`add-log-exp`
6×	`pow1` `add-cbrt-cube` `tan-quot` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `fma-neg` `associate-r` `associate-l` `prod-diff`
1×	`frac-times` `+-commutative` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `flip--` `distribute-lft-out` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

9.0ms	(- 1 (* (tan x) (tan eps)))
15.0ms	(+ (tan x) (tan eps))
30.0ms	(* (tan x) (tan eps))
1.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

series921.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(- 1 (* (tan x) (tan eps)))
161.0ms	(+ (tan x) (tan eps))
141.0ms	(* (tan x) (tan eps))
449.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))) (- (tan x)))

simplify1.9s

Counts

87 → 87

Iterations

Iter	Nodes
3	3076
2	961
1	341
0	148

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 13.9b

localize56.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.2b	(exp (- 1 (* (tan x) (tan eps))))
3.5b	(fma (+ (tan x) (tan eps)) (/ 1 (log (exp (- 1 (* (tan x) (tan eps)))))) (- (tan x)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `add-log-exp`
6×	`pow1` `add-cbrt-cube` `tan-quot` `add-exp-log`
5×	`exp-sum`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`exp-prod` `fma-def` `associate-r` `associate-l` `prod-diff`
2×	`rem-exp-log`
1×	`frac-times` `+-commutative` `sum-log` `sub-neg` `flip3-+` `exp-diff` `diff-log` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod` `flip-+` `fma-udef` `distribute-lft-out` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

23.0ms	(+ (tan x) (tan eps))
29.0ms	(* (tan x) (tan eps))
19.0ms	(exp (- 1 (* (tan x) (tan eps))))
1.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (log (exp (- 1 (* (tan x) (tan eps)))))) (- (tan x)))

series839.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(+ (tan x) (tan eps))
124.0ms	(* (tan x) (tan eps))
175.0ms	(exp (- 1 (* (tan x) (tan eps))))
413.0ms	(fma (+ (tan x) (tan eps)) (/ 1 (log (exp (- 1 (* (tan x) (tan eps)))))) (- (tan x)))

simplify1.4s

Counts

87 → 87

Iterations

Iter	Nodes
3	3080
2	919
1	338
0	155

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.0b

regimes173.0ms

Accuracy

0% (0.3b remaining)

Error of 13.0b against oracle of 12.6b and baseline of 13.0b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	18
1	18
0	17

end0.0ms

sample15.1s

Algorithm

intervals

Results

7.9s	3322×	body	1280	valid
3.5s	1785×	body	640	valid
2.3s	633×	body	2560	valid
697.0ms	823×	body	320	valid
297.0ms	1114×	body	80	valid
173.0ms	323×	body	160	valid